Virtually all plastid (chloroplast) genomes are circular double-stranded DNA molecules, typically between 100 and 200 kb in size and encoding circa 80–250 genes. Exceptions to this universal plastid genome architecture are very few and include the dinoflagellates, where genes are located on DNA minicircles. Here we report on the highly deviant chloroplast genome of Cladophorales green algae, which is entirely fragmented into hairpin chromosomes. Short- and long-read high-throughput sequencing of DNA and RNA demonstrated that the chloroplast genes of Boodlea composita are encoded on 1- to 7-kb DNA contigs with an exceptionally high GC content, each containing a long inverted repeat with one or two protein-coding genes and conserved non-coding regions putatively involved in replication and/or expression. We propose that these contigs correspond to linear single-stranded DNA molecules that fold onto themselves to form hairpin chromosomes. The Boodlea chloroplast genes are highly divergent from their corresponding orthologs, and display an alternative genetic code. The origin of this highly deviant chloroplast genome most likely occurred before the emergence of the Cladophorales, and coincided with an elevated transfer of chloroplast genes to the nucleus. A chloroplast genome that is composed only of linear DNA molecules is unprecedented among eukaryotes, and highlights unexpected variation in plastid genome architecture.